Chapter 11. CONSTRUCTION 

 Class10 Construction Multiple Choice Questions and Solution :

SECTION = A

Q1. To draw a pair of tangents to a circle which are inclined to each other at an angle of 35° , it is required to draw tangents at the end points of those two radius of the circle, the angle between which is :    [ Examplar 2020 ]

      (a)  105°              (b) 70°             (c)  140°                (d)  145° 

Solution :  (d)  145°  

Q2. To divide a line segment AB in the ratio p : q ( p , q are positive integers) , draw a ray AX so that   is an acute angle and then mark points on ray AX at equal distance such that the minimum number of these points is : [Examplar 2020]

(a) greater of p and q           (b)  p+q            (c) p+q - 1              (d)  pq  

Solution : 

Q3. To divide a line segment AB in the ratio 5 : 7 , first a ray AX is drawn so that  is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is : 

      (a)  8                      (b)  10                            (c)  11                            (d)  12 

Solution :  ()  

Q4. To divide a line segment AB in the ratio 4 : 7 , a ray AX  is drawn first such that  is an acute angle and then the points   are located at equal distances on the ray AX and the point B is joined to :  [ Examplar 2020 ]

          (a)                        (b)                    (c)                       (d)   

Solution :   ()

Q5. To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that  is an acute angle, then draw a ray BY parallel to AX and the points   and    are located at equal distance on ray AX and BY respectively .Then the points joints are :  [ Exampar 2020]

     (a)  and              (b)  and          (c)  and       (d) and  

Solution :    ()

Q6. To draw a pair  of tangents to a circle which are inclined to each other at an angle of 60° ,it is required to draw tangents at end points of those two radii of the circle. the angle between them should be :  [Examplar 2020 ]

 (a)  135°                 (b)  90°                 (c) 60°               (d)  120°       

Solution :  (d) 120°                        

 Class10 Construction 3 Marks Questions and Solution : 

SECTION = C

Q1. Draw a line segment of lenght 7.6 cm and divide it in the ratio 5 : 8 . Measure the two parts .

Solution :  Given a line segment AB is 7.6 cm , we want to divide it in the ratio 5 : 8 ,where 5 and 8 are positive integers .  

Steps of construction : 

  (i) We draw the line segment AB of length 7.6 cm .

  (ii) We draw any ray AX making an acute angle with AB .

                     

(iii) We draw a ray BY parallel to AX by making  equal to  .

(iv) Locate the points   on AX and  on BY such that   .

(v)  We join    and this line intersect AB at P . 

    Then     

           

Measurement :        (by construction)

                

                        

                        

                         cm

                 and       cm

Q3. Draw a circle of radius 4 cm . Construct a pair of tangents to it, the angle between which is 60° . Also justify the construction . Measure the distance between the centre of the circle and the point of intersection of tangents . [ Examplar 2020]

Solution:  Steps of construction : 

         (i).  Draw a circle of radius 4 cm with centre O .

        (ii) Take points A and B are on the circle . Join OA and OB .

         

         (iii) Draw a line AP perpendicular to radius OA  and Also a line BP perpendicular to OB . 

        (iv) Draw  AOB = 120° at O .

        (v) Join A and B at P, to get two tangents .  So,  .

      Justification :

                      Here , OAP = 90° ,  OBP = 90°   and  AOB = 120°  

                         In quadrilateral APBO , we have

                           OAP + APB + OBP + AOB = 360°

                            

                             Verified. 

Q2. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths .

Solution: Steps of construction: 

   

    (i) We take a point O as centre and draw a circle of radius 6 cm .

    (ii) We draw a point A at a distance of 10 cm from the centre O .

    (iii)  Join OA and bisect it . let M be the mid-point of OA . 

     (iv) Taking M as centre and OM as radius and we draw a circle to intersect the circle with radius 6 cm at B and C .  

      (v) Join AB and AC . Then AB and AC are the required two tangents . 

         Measurement :   Here , OA = 10 cm  and OB = 6 cm 

                     In  we have , 

                     

                           

                  Therefore, the length of the tangents is 8 cm .

Q3. Draw a line segment AB of lenght 8 cm . Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm . Construct tangents to each circle from the centre of the other circle.

Solution :    Steps of construction : 

 

 (i) We draw a line segment AB = 8 cm .

   (ii) We draw a circle with centre A and radius 4 cm .

    (iii) We draw another circle with centre B and radius 3 cm .

    (iv) Let M be the mid-point of AB . Taking M as centre and AM (or BM) as radius, draw a circle . Let it intersect the two given circle at the points C , D , E and F .

     (v) Join AC , AD , BE and BF .Then AC , AD , BE and BF are the required two tangents .  

Q4. Draw a circle of radius 3 cm . Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre . Draw tangents to the circle from these two points P and Q .

Solution : 

Steps of construction : 

(i) Take a point O, we draw a circle of radius 3 cm .

(ii) Take two points P and Q on one of its extended diameter each at a distance of 7 cm (OP = OQ = 7 cm) from its centre .

(iii) Bisect OP and OQ . Let   and  be the mid-point of OP and OQ respectively .

(iv)  Taking  as centre and  as radius, we draw a circle and it intersect the given circle at the points A and B .

(v)   Taking  as centre and  as radius, we draw another circle and it intersect the given circle at the points C and D .

(vi) join AP , BP , CQ and DQ .Then AP , BP , CQ and DQ are the required four tangents .